2v^2-3v-5=(v-1)(v-1)

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Solution for 2v^2-3v-5=(v-1)(v-1) equation: 


Simplifying
2v2 + -3v + -5 = (v + -1)(v + -1)

Reorder the terms:
-5 + -3v + 2v2 = (v + -1)(v + -1)

Reorder the terms:
-5 + -3v + 2v2 = (-1 + v)(v + -1)

Reorder the terms:
-5 + -3v + 2v2 = (-1 + v)(-1 + v)

Multiply (-1 + v) * (-1 + v)
-5 + -3v + 2v2 = (-1(-1 + v) + v(-1 + v))
-5 + -3v + 2v2 = ((-1 * -1 + v * -1) + v(-1 + v))
-5 + -3v + 2v2 = ((1 + -1v) + v(-1 + v))
-5 + -3v + 2v2 = (1 + -1v + (-1 * v + v * v))
-5 + -3v + 2v2 = (1 + -1v + (-1v + v2))

Combine like terms: -1v + -1v = -2v
-5 + -3v + 2v2 = (1 + -2v + v2)

Solving
-5 + -3v + 2v2 = 1 + -2v + v2

Solving for variable 'v'.

Reorder the terms:
-5 + -1 + -3v + 2v + 2v2 + -1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Combine like terms: -5 + -1 = -6
-6 + -3v + 2v + 2v2 + -1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Combine like terms: -3v + 2v = -1v
-6 + -1v + 2v2 + -1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-6 + -1v + 1v2 = 1 + -2v + v2 + -1 + 2v + -1v2

Reorder the terms:
-6 + -1v + 1v2 = 1 + -1 + -2v + 2v + v2 + -1v2

Combine like terms: 1 + -1 = 0
-6 + -1v + 1v2 = 0 + -2v + 2v + v2 + -1v2
-6 + -1v + 1v2 = -2v + 2v + v2 + -1v2

Combine like terms: -2v + 2v = 0
-6 + -1v + 1v2 = 0 + v2 + -1v2
-6 + -1v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-6 + -1v + 1v2 = 0

Factor a trinomial.
(-2 + -1v)(3 + -1v) = 0


Subproblem 1
Set the factor '(-2 + -1v)' equal to zero and attempt to solve:

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

Simplifying
v = -2

Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {-2, 3}

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